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I guess they just want 

\(A = \pi r^2 = \pi \left(\dfrac{D}{2}\right)^2 \\ D=10 \Rightarrow A = \pi(5)^2 = 25\pi \approx 78.5\)

\(\text{A point on the line }y=-x+6 \text{ is given by }(x, -x+6)\\ \text{the squared distance between two points u and v is given by}\\ d^2(u,v)=(u_x-v_x)^2+(u_y-v_y)^2 \\ \text{if the distance between two points is equal so will the squared distance be, so}\\ d^2[(10,-10),(x,-x+6)] = d^2[(0,0),(x,-x+6)] \\ (10-x)^2 + (-16+x)^2 = x^2 + (-x+6)^2 \\ 2 x^2-52 x+356=2x^2-12 x+36 \\ 320=40x\\ x=8,~y=(-x+6) = -2\\ (x,y) = (8,-2)\)

The mathy way of doing this is noting that for a square the perimeter is a function of s while the area is a function of s² 

So an increase in the perimeter by a factor of K leads to an increase in area by a factor of K²

or in even more mathy terms, the area is directly proportional to the square of the perimeter

Another way of putting this is

\(\dfrac{A_1}{A_2} = \left(\dfrac{P_1}{P_2}\right)^2 \\ \dfrac{A_1}{A_2} = \left(\dfrac{12}{24}\right)^2 = \dfrac 1 4\)

\(\text{Probably the clearest way to do this is to note that}\\ \cos(\angle RPS)=\cos\left(\pi - \angle RPQ\right)=-\cos(\angle RPQ)\\ \cos(\angle RPQ)=\sqrt{1 -\sin^2(\angle RPQ)} = \sqrt{1-\frac{49}{625}} \\ \cos(\angle RPQ) = \sqrt{\dfrac{576}{625}}=\dfrac{24}{25},\text{ and thus}\\ \cos(\angle RPS)=-\dfrac{24}{25} \)

Its 2.25x + 1.5x > -307 <=>

<=> 3.75x > -307 <=> 

<=> x>- 307/3.75 or x> -81.8666...

I hope to help you!

I'm showing 841 unique centroids.

Thank you so much Chris

Thank you hectictar

Find and simplify (f(a+h) - f(a))/h for f(x)= 3x^2 -5

I got this on a test and it seemed like there wasn't enough information to solve and wondered if anyone else could

That is pretty cool  !!!

We have

f (a+ h)  = 3(a + h)^2 - 5  =   3 [ a^2 + 2ah + h^2  ] - 5    =

3a^2 + 6ah + 3h^2  - 5

f(a)  =  3(a)^2  -  5   =   3a^2  - 5

So

[ f(a + h)  - f(a) ] / h  =

[  (3a^2 + 6ah + 3h^2 - 5)  -  (3a^2 - 5)  ]   / h  =

[6ah + 3h^2] / h  =

h [ 6a  + 3h ] / h  =

6a  + 3h

Note  that if we let  h approach 0,  we get   6a  =  the derivative  of  3x^2 - 5   when x = a ]

A  = 14790

r = .069  / 12   =  23 / 4000

n = 48

P  =  14790 *(23/4000) *  [ 1 + 23/4000]^(48) ] / [ ( 1 + 23/4000)^48  - 1 ] = 353.48 

So..."C"

Nice, hectictar  !!!

The 110° angle  will subtend a major arc of  twice its measure  = 220°

So...the remaining minor arc subtended by its endpoints = 360 -  220  = 140° 

The  105° angle will subtend a major arc of twice its measure = 210°

So...the remaining minor arc subtended by its endpoints  = 360 - 210  = 150°

So....the major arc intercepted by  the enpoints of  α  =  150 + 140  = 290°

And its measure is  1/2  of this   =  1/2 * 290   = 145°

The correct answer is B, "39.8 and approximately 79.6% of voters are dissatisfied with Congress". I hope this helps! 

The correct answer (I just took this test) is D, "Generate 100 numbers randomly using the digits 0 through 9, select 0 through 4 to represent a success and the digits 5 through 9 to represent not a success, run the trial 200 times, and plot the results on a proportion-frequency dot plot". This is because it states that the sample size is 100, so you must have 100 numbers, and the trial size is 200 so you must run it 200 times. The 0-4 were chosen to be successes because they were the ones that fit the data most. 

A   =  P  [ (1 + r)^n  - 1 ]

         _______________     

          r  ( 1 + r)^n

Where P  = 725    r  = .0825/12  = 11/1600    n  = 48 months

So  we  have

A = 725 [ (1 + 11/1600)^(48)  - 1 ]

      __________________________    ≈  29,555.11  ⇒  "B" seems the closest

         [ (11/1600) * ( 1 + 11/1600)^48

The answer is "B". Can you calculate it using the formula given to you? Try it.

The answer is "C". Can you calculate it using the formula given to you? Try it.

Solve for x:
4 x^2 + 48 x + 44 = 924

Write the quadratic equation in standard form.
Divide both sides by 4:
x^2 + 12 x + 11 = 231

Solve the quadratic equation by completing the square.
Subtract 11 from both sides:
x^2 + 12 x = 220

Take one half of the coefficient of x and square it, then add it to both sides.
Add 36 to both sides:
x^2 + 12 x + 36 = 256

Factor the left hand side.
Write the left-hand side as a square:
(x + 6)^2 = 256

Eliminate the exponent on the left-hand side.
Take the square root of both sides:
x + 6 = 16 or x + 6 = -16

Look at the first equation: Solve for x.
Subtract 6 from both sides:
x = 10 or x + 6 = -16

Look at the second equation: Solve for x.
Subtract 6 from both sides:
 x = 10 or x = -22 - discard this one. The dimensions of the Cuboid are:

4 cm,  10+1 =11 cm,  10+11 =21 cm

thanks for the trial of my pay

∠AEB  ≅  ∠CED   because they are vertical angles

∠EAB  ≅  ∠ECD   because they are alternate interior angles

So by the AA similarity theorem, △EAB ~ △ECD

Since △EAB ~ △ECD,

CD / AB  =  DE / BE

100 / 150  =  DE / BE

2 / 3  =  DE / BE

∠BCD  ≅  ∠BFE   because they are corresponding angles

∠BDC  ≅  ∠BEF   because they are corresponding angles

So by the AA similarity theorem, △BCD ~ △BFE

Since △BCD ~ △BFE,

DC / EF  =  BD / BE                       And    DC  = 100     and     BD  =  BE + DE

100 / EF  =  (BE + DE) / BE           Distribute  1 / BE  to the terms in parenthesees.

100 / EF  =  BE / BE + DE / BE

100 / EF  =  1 + DE / BE                And  DE / BE  =  2 / 3

100 / EF  =  1 + 2 / 3

100 / EF  =  5 / 3                Multiply both sides of the equation by  3 .

300 / EF  =  5                     Multiply both sides of the equation by  EF .

300  =  5 * EF                    Divide both sides of the equation by  5 .

60  =  EF

The number of centimeters in the length of EF is  60 .

Let the num of people John surveyed  =  p

Let the num of people who thought rats carried diseases  =  d

Let the num of people who said rats carry rabies   =  r

86.8% of the people surveyed thought rats carried diseases. In other words...

the num of people who thought rats carried diseases  =  86.8% of the num of people John surveyed

d  =  86.8% of  p

d  =  86.8%  *  p

d  =  86.8/100  *  p

d  =  0.868p

45.7% of the people who thought rats carried diseases said that rats frequently carried rabies.

r  =  45.7% of d

r  =  0.457d

Since rats do not frequently carry rabies, these 21 people were mistaken. So we know that the num of people who said rats carry rabies is 21. So we know  r = 21

r  =  0.457d                  We know  r  =  21 ,  so we can substitute  21  in for  r .

21  =  0.457d                And we know  d = 0.868p , so we can substitute  0.868p  in for  d .

21  =  0.457(0.868p)    Now we just have to solve this equation for  p .

21  =  0.396676p

21 / 0.396676  =  p

52.93993  ≈  p

John surveyed a total of  53  people.

Using Omi's diagram  and the exterior angle theorem, we have that

y  = x + 48      (1)

z   = y + x        (2)

Sub  (1)  into ( 2) for y   and we have

z  = ( x + 48 ) + x     

z  = 2x + 48

So..in the triangle on the right  

48 + x + z  = 180

48 + x + (2x + 48) = 180

96 + 3x  = 180

3x  = 180 - 96

3x  = 84

x = 28° =  angle "B"

Here is the answer.